Properties

Label 380.2.i
Level $380$
Weight $2$
Character orbit 380.i
Rep. character $\chi_{380}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 132 16 116
Cusp forms 108 16 92
Eisenstein series 24 0 24

Trace form

\( 16 q - 2 q^{3} - 4 q^{7} - 14 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{3} - 4 q^{7} - 14 q^{9} + 8 q^{11} + 6 q^{13} + 2 q^{17} + 10 q^{19} + 10 q^{23} - 8 q^{25} - 8 q^{27} - 2 q^{29} - 8 q^{31} + 16 q^{33} - 2 q^{35} - 56 q^{37} - 28 q^{39} - 16 q^{41} + 12 q^{43} - 8 q^{45} + 16 q^{47} + 32 q^{49} - 16 q^{51} + 24 q^{53} + 36 q^{57} + 18 q^{59} + 12 q^{61} + 6 q^{63} - 24 q^{65} + 10 q^{67} + 52 q^{69} + 8 q^{71} + 2 q^{73} + 4 q^{75} + 20 q^{77} - 18 q^{79} - 36 q^{81} - 20 q^{83} - 12 q^{87} - 14 q^{89} - 20 q^{91} - 4 q^{93} - 4 q^{95} - 24 q^{97} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.i.a $2$ $3.034$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(-8\) \(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-4q^{7}+\cdots\)
380.2.i.b $6$ $3.034$ 6.0.1783323.2 None \(0\) \(1\) \(3\) \(4\) \(q+(\beta _{3}-\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
380.2.i.c $8$ $3.034$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(-4\) \(0\) \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)